Added TrotterizedQfunc operation

[Jaybsoni]

Context:
One of the results from Discovery work in Product formulas was the need to generalize the TrotterProduct class such that it can work on exponentiated operators directly instead of system hamiltonians. This was to support the Compressed Double Factorization (CDF) technique on hamiltonians.

Description of the Change:

• Added new TrotterizedQfunc class
• Added new trotterize function

Benefits:

• Allows users to perform product formula based hamiltonian simulation on CDF hamiltonians.
• Generalizes the TrotterProduct class to the case where we have oracle access to the exponentiated terms of the hamiltonian.

Possible Drawbacks:

• Not sure how well it plays with program capture
• Not sure how well it integrates with catalyst and jax.jit

Related GitHub Issues:
None

[github-actions]

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Please edit doc/releases/changelog-dev.md with:

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[Jaybsoni]

[sc-72601]

[willjmax]

Looks good! Here are a few comments.

[soranjh]

Thanks @Jaybsoni, left some comments, will approve after that.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.64%. Comparing base (c5fd5bc) to head (c142695).
Report is 285 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6627      +/-   ##
==========================================
- Coverage   99.64%   99.64%   -0.01%     
==========================================
  Files         469      468       -1     
  Lines       44331    44125     -206     
==========================================
- Hits        44173    43967     -206     
  Misses        158      158              

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[albi3ro]

changelog?

[DSGuala]

Left a few comments, approved once they are addressed 🙂

[albi3ro]

Thanks :)

We can have a follow up to integrate this with capture, since it might be a bit more difficult.

[PietropaoloFrisoni]

Thanks @Jaybsoni! Can you please link the Shortcut story to this PR? 🙏